Filters of residuated lattices and triangle algebras
type: Item
instance of: scholarly article
title: Filters of residuated lattices and triangle algebras
zbMATH Open document ID: 1206.03058
published in: Information Sciences
publication date: 2010-09-02T00:00:00Z
full work available at URL: https://biblio.ugent.be/publication/1024646
review text: This paper presents in a very systematic and organized way some definitions and results on filters of residuated lattices, like for example prime filters, prime filters of the second and of the third kind, Boolean filters and Boolean filters of the second kind, and related properties on the quotients. Many useful examples on finite residuated lattices are given. Such definitions are extended to triangle algebras, which are interesting algebraic structures, introduced by the authors in [Fuzzy Sets Syst. 159, No.~9, 1042--1060 (2008; Zbl 1174.03028)], corresponding to interval-valued residuated lattices. Some results are given for these structures.
reviewed by: Brunella Gerla
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 06F05
zbMATH DE Number: 5777796
zbMATH Keywords: filters
zbMATH Keywords: residuated lattices
zbMATH Keywords: interval-valued structures
zbMATH Keywords: triangle algebras
author: B. Van Gasse
author: G. Deschrijver
author: C. Cornelis
author: E. E. Kerre
MaRDI profile type: Publication
OpenAlex ID: W2033750649
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DOI: 10.1016/J.INS.2010.04.010
description: scientific article; zbMATH DE number 5777796